Police in Australia are considering using fingerprinting to identify Muslim women wearing full veils after a court case in which a woman was let off because police could not be sure who she was.

The sensitive issue of women wearing the burka was thrust back into the spotlight this earlier this week when a magistrate dismissed a case against Carnita Matthews, 47, who had been accused of making a false complaint against the police.

Last year Miss Matthews was sentenced to six months' jail for falsely claiming that a highway patrol officer had tried to remove her burka when he stopped her for a random breath test.

But during her appeal it emerged that, because the complainant was wearing a burka when she appeared at a Sydney police station to report the incident, officers could only see her eyes, and ultimately could not be sure that Miss Matthews was the woman who made the false claim.

Miss Matthews's barrister, Phillip Boulten SC, told the court: "All we know is that a woman in a black burka came with a man in a brown suit with an envelope, and that's it."

Judge Clive Jeffreys allowed the argument, ruling that he was "not satisfied beyond reasonable doubt that she made the complaint." Following the decision, Mike Gallacher, the New South Wales police minister, said he would ask police to chow people wearing the burka – which covers the whole body except the eyes and hands – could be better identified.

One option, to be used when anyone refused to show their face because of religious reasons, was to provide a fingerprint, which could also be used on statutory declarations and other statements to ensure they were authentic, he said.

The proposal has the support of Barry O'Farrell, the state's premier.

Last year the debate over the burka became heated in Australia when a Muslim woman said she would feel uncomfortable giving evidence in a A$1 million (£576,000) fraud trial unless she were able to wear the full veil.

The woman had lived in Australia for seven years and had worn the burka since the age of 17, but the court denied her request and ordered her to testify without the veil.

The issue prompted one conservative senator to call for the burka to be banned because it was "unAustralian". However, Julia Gillard, the Australian prime minister, said she did not support a ban.

The full veil is banned in France and Belgium, but enforcing the bans has become difficult. Last week the first women to be summoned before a European court for illegally wearing the garments were refused entry, because they would not remove their face coverings.